Work and Pensions Secretary David Blunkett has said his family will sell shares he bought in a DNA testing firm.
Tony Blair says the matter is now closed
Mr Blunkett has denied claims of a potential conflict of interest over the shares in a company expected to bid for government contracts.
But in a written statement, he said he had asked his sons to approve disposing of the shares to avoid "continuing misinterpretation of the position".
Tony Blair says "the matter is closed". The Tories still want an inquiry.
A spokesman said no profit would be made from the sale of the shares - reported to be worth about £15,000 - but the details have yet to be finalised.
The row centres on Mr Blunkett's appointment as director of DNA Bioscience before May's general election, while he was out of the Cabinet, and his holding of shares in the firm.
He was in the job for a fortnight, resigning when he was appointed work and pensions secretary.
Mr Blunkett accepts he should have consulted an advisory committee when he took a directorship at DNA Bioscience - as ex-ministers are expected to do.
The prime minister asked Cabinet secretary Sir Gus O'Donnell to look into claims Mr Blunkett had broken the ministerial code by not asking the committee's advice.
In a letter released on Monday evening, Sir Gus tells Mr Blunkett he should have contacted the advisory committee but did not have to take its advice.
He is now taking steps to ensure the guidelines are clearer in future.
In another letter to the Conservatives, Sir Gus tells the Conservatives it is not for him to comment on whether the code had been broken.
He also says DNA Bioscience does not have any contracts with Mr Blunkett's department or the Child Support Agency. Nor is the firm in talks with them about future work.
The Tories say Mr Blunkett's directorship of the company constituted a conflict of interest because the firm is expected to bid for government contracts.
However, in his statement, Mr Blunkett said there had been "no conflict of interest".
He said he had made no representations to the government on behalf of DNA Bioscience since returning to the Cabinet, nor provided any advice to the company.
Mr Blunkett said that when he became work and pensions secretary he had told the chief civil servant in his department about his "short time" with DNA Bioscience and the shares.
He had also notified the MPs' register of members' interests.
"However, I am not prepared even to have the appearance that there could be any potential future conflict whilst the trust retains any shares in DNA Bioscience," he said.
His sons had now agreed to dispose of the shares, he said.
"I have taken this step not only to avoid continuing misinterpretation of the position, but also to protect family and friends from further intrusion and hope that will be respected."
Mr Blair earlier voiced confidence and his spokesman said the prime minister now believes no further action is needed.
But pressure from the Conservatives and the Liberal Democrats continues.
Shadow Commons leader Chris Grayling said he still wanted an inquiry into Mr Blunkett's actions.
"I continue to hold the view that I think Mr Blunkett's judgement has been so lacking that I don't see how he can remain in office," he said.
Lib Dem spokesman David Laws welcomed Mr Blunkett's decision to sell the shares.
"But he should be in no doubt that that he has now used up eight of his nine lives," said Mr Laws.
"Any further blunders would make Mr Blunkett's position untenable."
Mr Blunkett stepped down as home secretary last year over claims his office had fast-tracked a visa application for his lover's former nanny.